Microfluidics of Nematic Liquid Crystals and Nematic Colloids

Fig. 1: (a) Microfluidic channel fabricated by bonding a PDMS relief on a glass substrate. (b) Schematic representation of the microfluidic channel. (c) Magnified view of a sample region within the channel. Different colours of the nematic molecules indicate the degenerate planar surface anchoring on each of the channel walls. Zoom Image
Fig. 1: (a) Microfluidic channel fabricated by bonding a PDMS relief on a glass substrate. (b) Schematic representation of the microfluidic channel. (c) Magnified view of a sample region within the channel. Different colours of the nematic molecules indicate the degenerate planar surface anchoring on each of the channel walls.

Recent Review:
Liquid crystal microfluidics: surface, elastic and viscous interactions at microscales
A. Sengupta, S. Herminghaus, and Ch. Bahr, Liquid Crystals Reviews 2, 73 (2014).
DOI: 10.1080/21680396.2014.963716
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Novel colloidal systems consisting of micrometer-sized particles dispersed in nematic liquid crystals have recently attracted large interest [I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, S. Zumer, Science 313, 954 (2006)]. In these systems, the colloidal pair interaction is not of the van der Waals or electrostatic type, but stems from the elasticity of the director field of the nematic host. A direct manipulation of these systems can be achieved by means of optical tweezers. A different manipulation approach could be the use of forces which are present when the system flows through an appropriate microfluidic device. Although the influence of flow on the nematic volume phase has been studied theoretically and experimentally since the early 1970s, the study of nematic liquid crystals in the field of microfluidics is still at an early stage and a systematic study of the influence of the channel dimensions and geometry, the anchoring conditions on the channel walls, the magnitude of the flow rate, or other parameters does not exist.

We thus started with the study of a pure (without colloidal particles) nematic phase flowing through simple straight microchannels. The channels, prepared by bonding a PDMS relief on a glass substrate, had a rectangular cross section (width 50 - 100 micrometer, depth 5 - 30 micrometer). The plasma treatment, which is needed to bond the glass substrate to the PDMS relief, causes degenerate planar anchoring conditions on both the glass and the PDMS surface and for our initial studies we did not modify these conditions. Thus, near all four channel walls, the liquid crystal molecules prefer to align parallel to a wall but there is no preferred alignment direction within the plane of the wall. The nematic phase in the microchannel is studied by polarizing optical microscopy and fluorescence confocal optical microscopy.

Fig. 2: Evolution of nematic textures and topological defect structures as a function of the flow velocity and channel depth. (a) Topological singularities on channel surfaces get connected by a disclination line which undergoes simultaneous length reduction and transport under imposed flow. By increasing the Ericksen number (i.e., by either increasing the flow rate or decreasing the channel depth), four distinct textures were identified between crossed polarizers: (b) π-walls, (c) π-wall with a disclination line pinned to the channel wall, (d) disclination line with one end pinned and one freely floating end and (e) disclination loops flowing in a chaotic-like regime. (f) Occurrence of the different nematic textures on variation of flow velocity and channel depth. The combination of small velocity and low channel depth, corresponding to a low Ericksen number, results in the creation of π-walls. The inset shows the dependence of texture regimes on volume flow rate and channel depth. Zoom Image
Fig. 2: Evolution of nematic textures and topological defect structures as a function of the flow velocity and channel depth. (a) Topological singularities on channel surfaces get connected by a disclination line which undergoes simultaneous length reduction and transport under imposed flow. By increasing the Ericksen number (i.e., by either increasing the flow rate or decreasing the channel depth), four distinct textures were identified between crossed polarizers: (b) π-walls, (c) π-wall with a disclination line pinned to the channel wall, (d) disclination line with one end pinned and one freely floating end and (e) disclination loops flowing in a chaotic-like regime. (f) Occurrence of the different nematic textures on variation of flow velocity and channel depth. The combination of small velocity and low channel depth, corresponding to a low Ericksen number, results in the creation of π-walls. The inset shows the dependence of texture regimes on volume flow rate and channel depth.

By varying the flow rate and/or the vertical dimension of the channel, different forms of flow- and confinement-induced textures and topological defect structures evolve. For small channel depths of 5 - 10 μm, we observe with increasing flow rate the following sequence of structures: disclination lines connecting the top and bottom walls of the channel (and thus oriented perpendicular to flow) moving in the direction of flow leaving a set of parallel π-walls behind (Fig. 2b), disclination lines aligned parallel to the flow direction and pinned with both ends on a channel wall (Fig. 2c), disclination lines, aligned parallel to the flow direction, with one end pinned on a channel wall and one freely floating end (Fig. 2d), and a chaotic-like regime in which disclination lines and loops are freely floating, intertwining, annihilating and crossing each other (Fig. 2e). The same sequence of structures is observed when the depth of the channel is increased at constant flow rate.

Current studies are concerned with the evolution and morphology of the π-walls. A π-wall separates regions which differ by the orientation of the nematic director by an angle of π. It is not a real "wall" since the director orientation changes continuously when going from one region to another. In the microchannel, the π-walls are created by the impact of flow on disclination lines of strength ±1 or ±1/2. The disclination lines, which extend from the top to the botton of the channel, are moved downstream by the flow and leave a set of parallel π-walls behind which extend up to several hundred micrometers in length. They appear as alternating dark and bright stripes between crossed polarizers (Fig. 3d). The detailed structure of the π-walls can be manipulated to some extent by varying flow rate and direction.

Fig. 3: Creation of π-walls by a disclination line of strength -1 moving along the flow of the nematic liquid crystal. The disclination line is parallel to the z-coordinate, i.e., it connects the bottom and the top wall of the shallow microchannel. The following images show the xy-plane. (a) Unpolarized micrograph: the dark point indicates the scattering of light by the disclination line (perpendicular the image plane) at the leading end of the forming π-wall structure. (b) Micrograph between crossed polarizers: the alternate dark and bright regions are caused by the continuous change of the director orientation. (c) Schematic representation of director field in the xy-plane. (d) After the passing of several disclinations, the microchannel is filled with several parallel π-wall sets. Zoom Image
Fig. 3: Creation of π-walls by a disclination line of strength -1 moving along the flow of the nematic liquid crystal. The disclination line is parallel to the z-coordinate, i.e., it connects the bottom and the top wall of the shallow microchannel. The following images show the xy-plane. (a) Unpolarized micrograph: the dark point indicates the scattering of light by the disclination line (perpendicular the image plane) at the leading end of the forming π-wall structure. (b) Micrograph between crossed polarizers: the alternate dark and bright regions are caused by the continuous change of the director orientation. (c) Schematic representation of director field in the xy-plane. (d) After the passing of several disclinations, the microchannel is filled with several parallel π-wall sets.
Fig. 4: Capture of a colloidal particle (diameter 5 μm) by a disclination line which is aligned parallel to the flow direction of the nematic liquid crystal; once the particle is trapped, it follows the course of the disclination. The time difference between the micrographs is 0.1 seconds. Zoom Image
Fig. 4: Capture of a colloidal particle (diameter 5 μm) by a disclination line which is aligned parallel to the flow direction of the nematic liquid crystal; once the particle is trapped, it follows the course of the disclination. The time difference between the micrographs is 0.1 seconds.

Preliminary studies of nematic liquid crystals containing colloidal particles have shown that the flow-induced structures like π-walls and disclination lines can be used to guide the transport of the particles through the microchannels (Fig. 4). A key point for the continuation of these studies will be the use of channels possessing other anchoring conditions (unidirectional planar, homeotropic, tilted) on the channels walls, since the anchoring of the nematic director will essentially determine the details of the flow-induced structures.



Find more information:

Nematic Liquid Crystals and Nematic Colloids in Microfluidic Environment
A. Sengupta, S. Herminghaus, and Ch. Bahr, Mol. Cryst. Liq. Cryst. 547, 203 (2011).
DOI: 10.1080/15421406.2011.572784

Nematic textures in microfluidic environment
A. Sengupta, U. Tkalec, and Ch. Bahr, Soft Matter 7, 6542 (2011).
DOI: 10.1039/C1SM05052D

Fig. 5: Random planar anchoring (left column) and unidirectional planar anchoring (right column) in microchannels. The alignment in the unidirectional case is parallel to the channel axis. a,b: Polarizing microscopy images with two different orientations of the crossed polarizers. c: Fluorescence confocal polarizing microscopy images (laser polarization indicated by the doubleheaded white arrow). The high fluorescence signal (yellow color) confirms the alignment of the liquid crystal molecules along the channel axis. Scale bars correspond to 15 μm (left column) or 20 μm (right column).  Zoom Image
Fig. 5: Random planar anchoring (left column) and unidirectional planar anchoring (right column) in microchannels. The alignment in the unidirectional case is parallel to the channel axis. a,b: Polarizing microscopy images with two different orientations of the crossed polarizers. c: Fluorescence confocal polarizing microscopy images (laser polarization indicated by the doubleheaded white arrow). The high fluorescence signal (yellow color) confirms the alignment of the liquid crystal molecules along the channel axis. Scale bars correspond to 15 μm (left column) or 20 μm (right column). 

Functionalization of microchannel walls for defined anchoring conditions

The above described results were obtained with microchannels possessing random planar anchoring conditions on the surfaces of the channel walls. Random planar anchoring is the native anchoring condition of PDMS/glass microchannels prepared by plasma bonding. It is clearly desirable to obtain other anchoring conditions since the properties of confined liquid crystals are essentially influenced by their anchoring on the boundaries of the sample. We have developed experimental techniques in order to obtain well-defined anchoring conditions (homeotropic, unidirectional planar, hybrid conditions) on walls of standard PDMS/glass microchannels. Especially for the unidirectional planar case, the conventional methods which involve a mechanical treatment (rubbing) of the surface cannot be transferred to microchannels.

In order to achieve an unidirectional planar anchoring, we employ the photoalignment method using the polymer PVCN-F [I. Gerus, A. Glushchenko, S.-B. Kwon, V. Reshetnyak, and Y. Reznikov, Liq. Cryst. 28, 1709 (2001)], i.e., the channel walls are coated with a prepolymer which is then polymerized by polarized UV light. The orientation of the UV light polarization determines the direction of the alignment of the liquid crystal.

Find more information:

Functionalization of microfluidic devices for investigation of liquid crystal flows
A. Sengupta, B. Schulz, E. Ouskova, and Ch. Bahr, Microfluid. Nanofluid. 13, 941 (2012).
DOI: 10.1007/s10404-012-1014-7

Steering the flow in homeotropic microchannels

In microchannels with homeotropic anchoring conditions on all walls, a strong competition between the aligning effects of the boundaries and the flow exists. At low flow speeds, the director field is mainly determined by the anchoring on the channel walls, whereas at high flow velocities the major part of the director field is aligned along the flow direction. In between, at medium flow velocities,we observe a complex pattern in the director field and a non-Poiseuille velocity profile. Figures 6A-C illustrate our experimental observations concerning the director field in the three flow regimes and show results of numerical simulations (carried out by Miha Ravnik and Julia Yeomans) confirming the experiment. Figure 7 gives the flow velocity profiles in the three regimes.

Fig. 6: Three basic flow regimes in the homeotropic microchannel - (A) weak flow, (B) medium flow, and (C) strong flow. For each regime, the first row (a) shows experimental and calculated POM (polarizing optical microscopy) micrographs in the xy plane; the second row (b) shows experimental and calculated FCPM (fluorescence confocal polarizing microscopy) micrographs in the xy and yz planes including the director configuration at the half-depth of the channel, 0 and 1 respectively indicate nematic director orthogonal and parallel to the excitation laser polarization; the third row (c) shows the full director profile calculated across the channel cross-section for the three regimes, blue color indicates out-of-plane director orientation, whereas red color corresponds to in-plane director orientation. Experiments were performed in a 16 μm deep channel.  Zoom Image
Fig. 6: Three basic flow regimes in the homeotropic microchannel - (A) weak flow, (B) medium flow, and (C) strong flow. For each regime, the first row (a) shows experimental and calculated POM (polarizing optical microscopy) micrographs in the xy plane; the second row (b) shows experimental and calculated FCPM (fluorescence confocal polarizing microscopy) micrographs in the xy and yz planes including the director configuration at the half-depth of the channel, 0 and 1 respectively indicate nematic director orthogonal and parallel to the excitation laser polarization; the third row (c) shows the full director profile calculated across the channel cross-section for the three regimes, blue color indicates out-of-plane director orientation, whereas red color corresponds to in-plane director orientation. Experiments were performed in a 16 μm deep channel. 
Fig. 7: Flow profiles of the weak, medium, and strong flow regimes. (a) Experimental flow profiles at the half-depth of the channel. One stream flow is dominant in the low and high flow regimes. Two stream flow is observed in the medium flow regime. (b) Flow profiles at half-depth for the three regimes obtained from numerical modeling.  Zoom Image
Fig. 7: Flow profiles of the weak, medium, and strong flow regimes. (a) Experimental flow profiles at the half-depth of the channel. One stream flow is dominant in the low and high flow regimes. Two stream flow is observed in the medium flow regime. (b) Flow profiles at half-depth for the three regimes obtained from numerical modeling. 

In the low/medium velocity range, one can use the onset of the deformation of the director field for a direct visualization of the velocity field because the effective birefringence of the liquid crystal in the microchannel increases with the flow velocity. This is nicely demonstrated in a channel possessing a gradient in its width, and thus a gradient (of opposite sign) in the flow velocity along the channel axis. Figure 8 shows polarizing microscopy images for zero flow (no effective birefringence) and low flow (interference colors because of a spatially varying effective birefringence). With increasing volume flow rate, several orders of interference colors, similar to a Michel-Levy chart, can be observed (Fig. 9). With a single calibration, using e.g. particle tracking velocimetry, one can map a certain flow velocity to each interference color, enabling a simple determination of the velocity field in arbitrary channels possessing the same depth.

Fig. 8: (a) Polarizing optical microscopy (top row) and fluorescence confocal polarizing microscopy (middle row) micrographs of a channel filled with 5CB in absence of any flow. (b) At low flow rates, colorful birefringent domains appeared. The FCPM micrograph shows gradual decay of the signal along the downstream direction. The laser was polarized along the flow direction.  Zoom Image
Fig. 8: (a) Polarizing optical microscopy (top row) and fluorescence confocal polarizing microscopy (middle row) micrographs of a channel filled with 5CB in absence of any flow. (b) At low flow rates, colorful birefringent domains appeared. The FCPM micrograph shows gradual decay of the signal along the downstream direction. The laser was polarized along the flow direction. 
Fig. 9: (a) Polarizing micrographs showing the evolution of the birefringent domains with gradual increase of the volume flow rate as observed within the region marked in the inset (b).  Zoom Image
Fig. 9: (a) Polarizing micrographs showing the evolution of the birefringent domains with gradual increase of the volume flow rate as observed within the region marked in the inset (b). 


Find more information:

Liquid crystal microfluidics for tunable flow shaping
A. Sengupta, U. Tkalec, M. Ravnik, J. M. Yeomans, Ch. Bahr, and S. Herminghaus, Phys. Rev. Lett. 110, 048303 (2013).
DOI: 10.1103/PhysRevLett.110.048303

Opto-fluidic velocimetry using liquid crystal microfluidics
A. Sengupta, S. Herminghaus, and Ch. Bahr, Appl. Phys. Lett. 101, 164101 (2012).
DOI: 10.1063/1.4760276

Fig. 10: Hybrid anchoring (homeotropic on the three PDMS walls, uniform planar on the glass wall, top image) results in the formation of a disclination line (bottom). The strength of the disclination can be +1/2 (not shown) or -1/2.  Zoom Image
Fig. 10: Hybrid anchoring (homeotropic on the three PDMS walls, uniform planar on the glass wall, top image) results in the formation of a disclination line (bottom). The strength of the disclination can be +1/2 (not shown) or -1/2. 

Guided transport with topological microfluidics

Appropriate anchoring conditions on the channel walls result in the targeted generation of a disclination line that can be used as a soft rail for the transport of microfluidic cargo. The disclination is generated by homeotropic anchoring on three walls and uniform planar anchoring on the fourth wall (Fig. 10).

Without flow, the disclination is located near one of the sidewalls. The presence of a flow locates the disclination along the channel center axis, provided that the in-plane orientation of the director on the planar anchoring wall is perpendicular to the channel axes (as drawn in Fig. 10). By varying the angle φ between the in-plane director orientation and the channel axis one can tune the position of the disclination line in the channel (Fig. 11).

Fig. 11: Dependence of the disclination position on the relative angle φ between flow direction and the initial director orientation, referenced to the channel center. The polarization micrograph in the inset shows the gradual shift of the defect line (marked by the blue arrow) as φ changes, anchoring is along the direction of the double-headed red arrow; scale bar: 100 μm.  Zoom Image
Fig. 11: Dependence of the disclination position on the relative angle φ between flow direction and the initial director orientation, referenced to the channel center. The polarization micrograph in the inset shows the gradual shift of the defect line (marked by the blue arrow) as φ changes, anchoring is along the direction of the double-headed red arrow; scale bar: 100 μm. 

By using the relation between φ and the position of the disclination in the channel, one can control the course of the disclination at a channel bifurcation. It is also possible to switch the disclination line in situ between two arms of a bifurcation, as is demonstrated in the following video:

Video 1: In situ switching of a disclination line.

The use of the disclination as a soft rail is demonstrated by the following videos. Solid particles as well as aqueous droplets are trapped by the disclination line and then guided along, following the course of the disclination through the microchannel.

Video 2: Trapping and transport of a colloidal chain of three particles.
Video 3: Transport of aqueous droplets.


For more information on this novel approach to guided transport of microfluidic cargo based on topological microfluidics see the following paper:

Topological microfluidics for flexible micro-cargo concepts
A. Sengupta, Ch. Bahr, and S. Herminghaus, Soft Matter 9, 7251 (2013).
DOI: 10.1039/c3sm50677k (open access)

 
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